Where It All Goes Down
The Underworld and the Royal courts of Spain and Portugal
Our tragedy bounces back-and-forth between Spain and Portugal, but the most far-flung region explored is the pagan underworld. Despite the fire, brimstone, and eternal punishment for all the baddies, Hell actually comes off downright civilized compared to the earthly locations in the play. In both Spain and Portugal, there's widespread corruption, no mercy, very few trusted allies, and lots and lots of murder.
So, why would Kyd make Spain and Portugal the setting for murder and mayhem? Because Spain was England's greatest rival at the time, that's why. We know that Kyd wrote The Spanish Tragedy in the mid to late 1580s, and all of you history buffs are probably already recalling that Spain invaded England in 1588. Or at least Spain tried to invade England. On their way to merry ol' England, The Spanish Armada (the biggest in the world at the time) ran into a storm just off the British coast, which enabled the much weaker English forces to send the Spaniards packing.
Defeating the mighty Spanish Armada was a home field advantage kind of win. And the years before and after the invasion were a time when xenophobia (hating on peeps from other countries) and nationalism reigned. By casting Spain as a bloodthirsty, lawless place, Kyd was capitalizing on England's deepest fears to spike theater attendance. Knowing that Londoners would have an Us-vs.-Them attitude while watching despicable acts in Spain will help you understand why all the violence seems so senseless.
So go ahead and think of the play as negative propaganda on a foreign enemy. Interestingly enough, there are no references to the defeat of the Spanish Armada in Kyd's play. This probably means the play was written prior to 1588. It's hard to believe that Kyd would pass up the opportunity to earn some easy applause by bringing up a big, underdog victory.
Light on the Details
Other than while we are in Hell (please don't touch the brimstone), we get very little detail about places. Spain and Portugal are cast as blank slates where the actions of their inhabitants are used to suggest national character. As for Hell, it's standardly hellish. Kyd was clearly thinking of Aeneas' descent into the underworld in Virgil's seminally important work, the Aeneid.
In the end, it's a voyage to Hell and back that will have you thinking fondly about returning to Hell. Think about that for a second.